April 12, 2014

Consider a computer simulation of a mini universe, a universe complex enough to give rise to sentient beings. As Greg Egan points out in Permutation City, (and as is obvious to anybody who has played The Sims), the subjective flow of time in the simulated universe could be many times faster or slower than ours. In fact, once we have the simulation going, we can fast forward, rewind back, play the frames out of order, and it wouldn't matter one bit to the subjective experience of the simulated folk. What if we stopped the simulation? What if we saved the whole history on a DVD and put it on a shelf? Again, the subjective experience of the simulated, which arise from the relationships between their successive moments, would be uneffected. We would just be missing the opportunity to observe them in action, and interact with them.

That brings us to the next natural question: do they need the simulation, the DVD, do they need us at all? Don't they just "exist" independently whether or not we happen to be watching, recording, interacting or anybody has ever thought of them? Max Tegmark advances the Mathematical Universe Hypothesis, which says (1) our universe at the most basic level IS (not just described by) a mathematical structure (an electron or a photon can be defined exactly by a handful of numbers and there is nothing left over), and that (2) any mathematically consistent (computable?) structure must exist in the same sense as we do!

Needless to say this has led to quite a bit of spirited discussion around the web, I would recommend Scott Aaronson's blog post and the comments therein.